Lines and Angles Class 6 Worksheet — Free PDF Download with Answers

Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. Whether you searched for a maths class 6 worksheet or a worksheet math class 6 resource, you have landed in the right place. SparkEd's Class 6 maths practice covers the full CBSE syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

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For revision before exams, try the maths worksheet for class 6th with answers alongside our maths mcq for class 6 with answers sets. Teachers can use the class 6 maths mcq question paper bank for quick classroom tests. Browse all class 6 maths worksheets cbse topics on the All Class 6 worksheets page, or start with the popular Number Play worksheet. Ready to practise? Head to SparkEd home and pick your chapter.

Want to practise Lines And Angles digitally? Try free online practice on SparkEd — instant grading, visual solutions, and an AI coach to help when you are stuck.

What are Lines and Angles?

Looking for a class 6 math worksheet or maths worksheet for class 6 with answers? This comprehensive resource covers everything you need. Lines and angles are the building blocks of geometry. A line extends infinitely in both directions and has no endpoints, while a line segment has two endpoints and a fixed length. A ray has one endpoint and extends infinitely in one direction. When two rays share a common starting point, they form an angle.

In Class 6, students learn to identify these geometric objects, classify angles by their measure, and understand relationships between angles such as complementary and supplementary pairs. This chapter lays the groundwork for everything from triangle properties in Class 7 to coordinate geometry in Class 10.

Beyond the classroom, angles are everywhere — in architecture, engineering, sports, and even art. Understanding how to measure and classify angles gives students a vocabulary for describing the physical world precisely.

Beyond this worksheet, SparkEd offers interactive online practice for Lines And Angles with step-by-step solutions and progress tracking — perfect for daily revision.

Key Concepts & Formulas

Core ideas to revise before the worksheet:

• Point — A location in space with no size. Denoted by a capital letter (e.g., $A$).
• Line — Infinite in both directions, denoted $\overleftrightarrow{AB}$.
• Line segment — Finite, denoted $\overline{AB}$, with a measurable length.
• Ray — One endpoint, extends infinitely, denoted $\overrightarrow{AB}$ (starts at $A$).
• Angle — Formed by two rays with a common vertex. Measured in degrees ($^\circ$).
• Types of angles:
• - Acute: $0^\circ < \theta < 90^\circ$
• - Right: $\theta = 90^\circ$
• - Obtuse: $90^\circ < \theta < 180^\circ$
• - Straight: $\theta = 180^\circ$
• - Reflex: $180^\circ < \theta < 360^\circ$
• Complementary angles — Two angles whose sum is $90^\circ$.
• Supplementary angles — Two angles whose sum is $180^\circ$.
• Perpendicular lines — Two lines meeting at $90^\circ$.
• Parallel lines — Two lines in the same plane that never meet.

How to Study Lines and Angles Effectively

How to Use This Worksheet

1. Print the PDF — Download using the links below. Keep a protractor, ruler, and pencil handy.
2. Start with Level 1 (Easy) — 20 questions on identifying lines, rays, segments, and classifying angles. Aim for near-perfect accuracy.
3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.
4. Check answers — Use the included answer key.
5. Revise mistakes — Redraw the figure for every wrong answer and label each element correctly.
6. Move to the next level — Progress when you score 16/20 or above.

Sample Questions

Level 1 — Easy

1. Classify the angle: $\angle P = 72^\circ$.
2. *Solution:* $0^\circ < 72^\circ < 90^\circ$, so it is an acute angle.
3. Name the line segment joining points $M$ and $N$.
4. *Solution:* $\overline{MN}$.
5. Two angles are supplementary. One is $110^\circ$. Find the other.
6. *Solution:* $180^\circ - 110^\circ = 70^\circ$.

Level 2 — Medium

1. The complement of an angle is $18^\circ$ more than the angle itself. Find the angle.
2. *Solution:* Let the angle be $x$. Then $x + (x + 18) = 90 \Rightarrow 2x = 72 \Rightarrow x = 36^\circ$.
3. Two lines intersect at point $O$. If one of the angles formed is $65^\circ$, find all four angles.
4. *Solution:* Vertically opposite angles are equal: $65^\circ, 115^\circ, 65^\circ, 115^\circ$.
5. Is it possible for two obtuse angles to be supplementary? Why?
6. *Solution:* No. Each obtuse angle is $> 90^\circ$, so their sum would exceed $180^\circ$.

Level 3 — Hard

1. Three lines meet at a point forming six angles. If two adjacent angles are $55^\circ$ and $40^\circ$, find all six angles.
2. *Solution:* The third angle adjacent to these two is $360^\circ - 2(55 + 40 + \text{third})$. Actually, three lines at a point create 6 angles. Opposite angles are equal. Third pair angle $= 180^\circ - 55^\circ - 40^\circ = 85^\circ$. Six angles: $55^\circ, 40^\circ, 85^\circ, 55^\circ, 40^\circ, 85^\circ$.
3. An angle is $\frac{1}{3}$ of its supplement. Find the angle.
4. *Solution:* Let angle $= x$. Supplement $= 180 - x$. Given $x = \frac{1}{3}(180 - x) \Rightarrow 3x = 180 - x \Rightarrow 4x = 180 \Rightarrow x = 45^\circ$.
5. In the figure, $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are opposite rays. $\overrightarrow{OC}$ makes $\angle AOC = 3x + 10$ and $\angle BOC = 2x + 20$. Find $x$.
6. *Solution:* Since $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are opposite rays, $\angle AOC + \angle BOC = 180^\circ$. So $3x + 10 + 2x + 20 = 180 \Rightarrow 5x = 150 \Rightarrow x = 30$.

Board-Wise Approach

CBSE (NCERT — Ganita Prakash / Math Magic)
The "Lines and Angles" chapter covers basic definitions, angle measurement with a protractor, and classification. CBSE emphasises hands-on activities like paper-folding to discover right angles and supplementary pairs. The Ganita Prakash textbook adds exploratory tasks.

ICSE (Selina / ML Aggarwal)
ICSE covers this under "Basic Geometry" or "Basic Geometrical Concepts." The treatment is similar but includes more construction-based questions (using compass and straightedge). ICSE exams often include numerical problems on complementary/supplementary angles alongside diagram-based identification.

IB MYP (Mathematics Framework)
The MYP "Geometry Basics" unit takes an investigative approach. Students explore angle relationships through real-world contexts (architecture, design) and are expected to justify their answers in writing. The focus is on reasoning rather than rote classification.

Key Differences:
* CBSE: Activity-based learning; protractor usage tested.
* ICSE: Construction questions included; more numerical problems.
* IB: Investigative and justification-oriented.

Download Worksheets

Download your free Lines and Angles worksheets:

• Lines and Angles CBSE Worksheet — 60 questions aligned to NCERT
• Basic Geometry ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online with instant feedback:

• Practice Online — CBSE
• Practice Online — ICSE
• Practice Online — IB

Each worksheet has 20 questions per level with a detailed answer key.

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